Question

1.   Given the following system equations of price (P) and quantity (Q) determination in a widget market:

SHOW ALL WORK!

Demand: Q = 100 - 4P + 2G …..(1)      

Supply:    Q= 60 + 10P – 3N ……(2)

Where the price of substitute good, G = 10, and the cost of production N = 8.

1-a) by using the repeated substitution method only, please find equilibrium P and Q.

1-b) if G is up by 2, shows the impact of changing N on P and Q.

Answer 1

Given that:

Demand: Q = 100 - 4P + 2G -- equation 1)

Supply:    Q = 60 + 10P – 3N -- equation 2)

If G = 10, and N = 8

1-a) Solution

Equilibrium will occur when:

D = S

Thus, equating 1) and 2)

100 - 4P + 2(10) = 60 + 10P – 3(8)

100 - 4P + 20 = 60 + 10P - 24

120 - 4P = 36 + 10P

120 - 36 = 14P

84 = 14P

P = $6

To find Q, substitute the value of P in equation 1)

Q = 100 - (4 x 6) + (2 x 10)

Q = 100 - 24 + 20

Q = 96 units

We may also verify the same by substituting P in equation 2)

Q = 60 + 10P - 3N

Q = 60 + (10 x 6) - (3 x 8)

Q = 120 - 24

Q = 96 units

Hence, equilibrium Price is $6, and Quantity is 96 units

1-b) If G is up by 2, the equilibrium P and Q will change as follows.

N will not change in this case. No information is provided on change in N.

The new value of G is now 12.

Equilibrium will occur when:

D = S

Thus, equating 1) and 2)

100 - 4P + 2(12) = 60 + 10P – 3(8)

100 - 4P + 24 = 60 + 10P - 24

124 - 4P = 36 + 10P

124 - 36 = 14P

88 = 14P

P = $6.286

To find Q, substitute the value of P in equation 1)

Q = 100 - (4 x 6.286) + (2 x 12)

Q = 100 - 25.144 + 24

Q = 98.86 ~ 99 units

We may also verify the same by substituting P in equation 2)

Q = 60 + 10P - 3N

Q = 60 + (10 x 6.286) - (3 x 8)

Q = 122.86 - 24

Q = 98.86 ~ 99 units

Hence, new equilibrium Price is $6.286, and Quantity is 99 units.

Due to the increase in price of substitute good, the quantity demanded of widgets will rise. This will cause a rise in the price of widgets. Sellers will also now be able to sell more widgets.